few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Standard options: 
A. Solve linear equations in one variable.
B. Analyze and solve pairs of simultaneous linear equations.


Thought: The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001392

8
options: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
problem_activity: Problem 1
At the candy store, M&Ms and Skittles are sold for $0.50 per ounce. Kevita puts some M&Ms in a bag and then adds 8 ounces of Skittles. The total cost for her bag of candy is $6.50.
Kevita and Mary write the equation
$${0.5(x+8)=6.50}$$
to represent the situation, where
$$x$$
represents the number of ounces of M&Ms.
Kevita says that to solve this equation, you first distribute the
$$0.5$$
through the parentheses to get
$${0.5x+4=6.50}$$
.
Mary says that to solve this equation, you first divide by
$$0.5$$
on both sides to get
$${x+8=13}$$
.
Do you agree with either Kevita or Mary? Why? Finish solving the problem to find out how many ounces of M&Ms Kevita put in her bag of candy.
Problem 2
The taxi fare in Gotham City is $2.40 for the first
$${1 \over 2}$$
mile and additional mileage is charged at the rate of $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10?
What are two different ways you can solve this problem?
Problem 3
The ages of three cousins are consecutive integers. The sum of their ages is 45. Calculate their ages.
a.   Draw a tape diagram to represent the ages of the cousins.
b.   Let the youngest cousin's age be represented as
$$x$$
years old. Write and solve an equation to find the ages of the cousins.


correct_option_index: 0

1